Answer :
Answer:
[tex]9^{-\frac{1}{2}}=\frac{1}{3}[/tex]Given:
[tex]9^{-\frac{1}{2}}[/tex]To evaluate this, we must be familiar with two exponent rules.
The first one is, the negative exponent tells us that a number with a negative exponent should be put to the denominator or vice versa. Therefore, we can rewrite the given expression as:
[tex]\frac{1}{9^{\frac{1}{2}}}[/tex]Then, fractional exponents states that:
[tex]a^{\frac{m}{n}}=\sqrt[n]{a^m}[/tex]Since we have m = 1, and n = 2, we can rewrite the expression as:
[tex]\frac{1}{\sqrt[2]{9^1}}=\frac{1}{\sqrt[]{9}}[/tex]Next, we simplify this equation by getting the square root of 9, which is 3. Therefore, the final expression would be:
[tex]\frac{1}{3}[/tex]